Homework Help:
Congruence problem

I first tried adding and got [tex]5x + 5y \equiv 5 mod 631[/tex], but I was then stuck, so I tried the old multiplication, which looked worse as: [tex]6x^2 + 13xy + 6y^2 \equiv 6 mod 631[/tex]

Any ideas? I am guessing that I need to go somewhere with the addition one, but I can't see where. The instructor had a hint of using the fact that 631 is prime, but I can't see anything from that. Thanks.

Hmm, just got an idea, [tex]5(x + y) \equiv 5 mod 631[/tex], then find inverse of 5 and multiply it through to find x+y = something mod 631. I did this and got:

[tex]x + y \equiv 5*79380 mod 631[/tex]
which is
[tex]x + y \equiv 1 mod 631[/tex]
Now where can I go from here? Any ideas?